归约树思想
每一步将活跃线程数减半
归约树思想 是 CoddyKit 上的免费 CUDA Academy 课时。 这是第 1 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 CUDA Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 CUDA Academy 课程共包含 4 节课。
本课时的部分内容尚未翻译，以英文显示。
What Reduction Means
A reduction collapses a whole array into one value, like summing every element down to a single total. It is one of the most common GPU patterns. 🌳
The Sequential Way Is Slow
On a CPU you add elements one after another. That is O(n) sequential steps, so a million numbers means a million dependent additions in a row.
Addition Is Associative
The trick is that addition is associative: (a+b)+c equals a+(b+c). So you are free to add pairs in any grouping you like.
Add in Parallel Pairs
Because grouping is free, you can add many independent pairs at the same time. Every thread handles one pair, all in a single parallel step.
Halving Each Step
After one pass, half the elements are gone. Repeat, and the active count keeps halving: 8 to 4 to 2 to 1.
Logarithmic Depth
Halving means you finish in log2(n) steps instead of n. A million elements collapses in about 20 steps, not a million.
Picture the Tree
Drawing the pairings makes a binary tree. Leaves are the inputs, each level halves the nodes, and the root is your final sum.
Stride Doubles Each Pass
One way to code it: each step a thread adds its neighbor at distance stride, and that stride doubles every pass through the data.
for (int s = 1; s < blockDim.x; s *= 2) {
if (tid % (2 * s) == 0)
data[tid] += data[tid + s];
__syncthreads();
}Sync Between Steps
Every level depends on the previous one finishing, so threads must wait at a barrier before reading their partner's result.
Work Versus Span
Total additions stay about n, the work. But the longest dependency chain, the span, shrinks to log2(n). Same work, far less waiting.
Not Just Summing
The same tree works for any associative operation: max, min, product, or logical AND. Swap the operator and the structure stays.
Quick Check
Think about how many parallel steps a tree reduction needs.
Recap
You learned the reduction tree: add pairs in parallel, halve each step, finish in log2(n). It works for any associative operator. Next, keep warps busy! 🎉
常见问题解答
「归约树思想」课时是免费的吗？
是的 — 「归约树思想」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 CUDA Academy 课程的其余内容，请升级到 CoddyKit PRO。 CUDA Academy 课程共包含 4 节课。
「归约树思想」这节课中我会学到什么？
每一步将活跃线程数减半 你通过在浏览器中直接运行的动手代码来练习 CUDA Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。
学习 CUDA Academy 需要有经验吗？
无需任何先前经验。CoddyKit 上的 CUDA Academy 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 1 节课，共 4 节。
「归约树思想」课时需要多长时间？
大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。
我能在这节 CUDA Academy 课中编写并运行代码吗？
能。每节 CUDA Academy 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。